Explicit Transfer Function of RC Polyphase Filter for Wireless Transceiver Analog Front-End

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1 Explici Transfer Funcion of RC Polyphase Filer for Wireless Transceiver Analog Fron-End H. Kobayashi, J. Kang, T. Kiahara, S. Takigami, H. Sadamura, Y. Niki, N. Yamaguchi EE Dep. unma Universiy, Japan

2 Conens Research oal Roles of RC Polyphase Filer Transfer Funcion Derivaion of RC Polyphase Filer - s -order filer - nd -order filer - rd -order filer Summary

3 Research oal To esablish sysemaic design and analysis mehods of RC polyphase filers. As is firs sep, o derive explici ransfer funcions of he s-, nd- and rd-order RC polyphase filers.

4 Roles of RC Polyphase Filer Wireless Transceiver 4

5 Feaures of RC Polyphase Filer s pu and oupu are complex signal. Passive RC analog filer One of key componens wireless ransceiver analog fron-end -, Q signal generaion - mage reecion s explici ransfer funcion has no been derived ye. 5

6 Firs-order RC Polyphase Filer Q- ou R C C Qou Q R C ou- - R C Qou- R Differenial Complex npu: V Q Differenial Complex Oupu: Vou ou Qou 6

7 , Q signal generaion from sgle susoidal pu cos LO Q 0 Polyphase Filer.5 ou ou A cos LO θ Qou A s LO θ Qou LO volage [V] ime [us] 7

8 Cose, Se Signals Receiver cos0 F Analog Bandpass Filer - s0 AD Converer AD Converer Q analog digial They are used for down conversion 8

9 Pure, Q signal generaion rd -order harmonics reecion coslob cos LO Q s LOB s LO Polyphase Filer ou A cosloθ Qou A sloθ Wih rd -order harmonics. Wihou rd -order harmonics. 9

10 Simulaion of rd -order harmonics reecion 8 Q Q Q ou ou cos s LO LO LO Acos As acos as LO LO θ θ LO LO volage [V] volage [V] ou ime [us] Qou ime [ns] 0

11 mage Reecion Filer AB cos Q A-B s Polyphase Filer ou Acos Qou As Ae Be Ae

12 Problem when LO /RC ou Qou LO volage [V] ime [us] ou Qou LO volage [V] Ampliudes of,q signals differ significanly. ime [us]

13 nd -order RC Polyphase Filer The problem of large difference beween ou, Qou ampliudes can be alleviaed C C C R R R R R C C C R C R C ou Qou R ou Qou Q - Q- ou- Qou- LO volage [V] ime [us]

14 rd -order RC Polyphase Filer The ampliude difference problem is furher alleviaed. C C C R R R R C C C C ou R C R R R Qou C C C R R R R C Q - Q- ou Qou ou- Qou- LO 4

15 Transfer Funcion Derivaion of RC Polyphase Filer 5

16 Transfer Funcion of RC Polyphase Filer Complex Signal Theory Complex pu Complex oupu V V ou ou Q Q ou Complex Transfer Funcion V ou V 6

17 7 Transfer Funcion of s -order RC Polyphase Filer Q V Q V Q Q Q Q Q Q ou ou ou ou ou ou ou ou ou Differenial signal Complex signal R C Q - Q- ou Qou ou- Qou- C C R R R C

18 Transfer Funcion of s -order RC Polyphase Filer Transfer Funcion RC. RC a RC RC RC 8

19 Nyquis Char of w X Y Symmeric wih respec o a le of Y -X. 9

20 0 Explanaion of, Q signal generaion by ] [ cos e e V 4 s 4 cos ] [ π π e e V ou 4, 0, π RC RC, cos 0, Q

21 Oupu Load CL Effecs RC RCCL Q - C C R R R ou CL Qou CL ou- CL Q- C R Qou- CL

22 npu mpedance npu mpedance Z Complex npu Volage Complex npu Curren Q - C C R R R C ou Qou ou- Q- C R Qou- Z RC C [RC]

23 Componen Mismach Effecs Mismaches Vou Vou where V V E δx : among R s, C s mage signal Vou is caused. E E δx δx V V RC Q C C C R R R R C mage ransfer funcion - Q- ou Qou ou- Qou-

24 Transfer Funcion of nd -order RC Polyphase Filer Transfer Funcion C R C R Derivaion is very complicaed, so we used Mahemaica. a characerisics 4

25 Nyquis Char of Symmeric wih respec o a le of X 0. X Y 5

26 Feaures of nd -order RC Polyphase Filer lim ±,, 0,, 0, 0, For arbirary a, a / a. 6

27 Fla passband design of nd -order RC Polyphase Filer Passband: ~ Sopband: - ~ - where : /RC, sopband passband : /RC To make ga passband fla,. mage Reecion Raio - 7

28 8 Explanaion why a nd -order filer reduces, Q ampliude difference. cos 0, e e Q s cos ] [ θ θ θ θ e e Q ou ou npu signal Oupu of a s -order filer

29 9 s cos ] [ θ θ θ θ e e Q ou ou >> Explanaion why a nd -order filer reduces, Q ampliude difference. Oupu of a nd -order filer Accordg o he ransfer funcions, hen, he ampliude difference is reduced. LO a

30 Transfer Funcion of rd -order RC Polyphase Filer N D R D where N D R [ D [ ] 0 ]

31 a, Phase of rd -order RC Polyphase Filer a: Phase: a characerisics an D D D D N R R

32 Nyquis Char of n case RCRC RC [Y] Symmeric wih respec o a le of Y X. [X] X Y

33 Summary Explici ransfer funcions of s-, nd- and rd-order RC polyphase filers. Sysemaic design and analysis are possible. On-gog proecs Derivaion of higher-order filer ones. Nonidealiy effecs higher-order filers. Sysemaic design mehod usg Nyquis char.

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